A113276 Decimal expansion of de Bruijn's constant.

1, 1, 0, 6, 4, 9, 5, 7, 7, 1, 4

Offset

1,4

Comments

From Amiram Eldar, Jun 22 2021: (Start)

The minimal number c such that for any sequence of nonnegative numbers b(k) the following inequality always holds: Sum_{k>=1} b(k) <= c * Sum_{k>=1} sqrt(Sum_{i>=k} b(i)^2/k).

Also called the Copson-de Bruijn constant after the British mathematician Edward Thomas Copson (1901-1980) and the Dutch mathematician Nicolaas Govert de Bruijn (1918-2012). (End)

References

R. P. Boas and N. G. de Bruijn, Solution for problem 83, Wiskundige Opgaven met de Oplossingen, Vol. 20 (1957), pp. 2-4.

N. G. de Bruijn, Asymptotic Methods in Analysis, New York: Dover, 1981. See p. 174.

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, pp. 217-219.

Links

Table of n, a(n) for n=1..11.

E. T. Copson, Note on Series of Positive Terms, J. London Math. Soc., Vol. 2 (1927), pp. 9-12.

E. T. Copson, Note on Series of Positive Terms, J. London Math. Soc., Vol. 3 (1928), pp. 49-51.

Eric Weisstein's World of Mathematics, de Bruijn Constant.

Example

1.1064957714...

Crossrefs

Sequence in context: A333322 A348896 A153630 * A086034 A191622 A021943

Adjacent sequences: A113273 A113274 A113275 * A113277 A113278 A113279

Keyword

nonn,cons,hard,more

Author

Eric W. Weisstein, Oct 21 2005

Status

approved